Question

Cho A = 1 +2 +2^2+2^3+ ....+ 2^11 

HÃy chứng tỏ  A chia hết cho 3

Answer 1

vì : A=(2+2²)+...........+(2⁵⁹+2⁶⁰)

       =2.(1+2)+..........+2⁵⁹.(1+2)

       =3.(2+2³+...........+2⁵⁹)

=> A chia hết cho 3

Answer 2

A=1+2+2²+2³+...+2¹¹

=> A= (1+2)+(2²+2³)+...+(2¹⁰+2¹¹)

=> A= 3+2².(1+2) + ...+ 2¹⁰.(1+2)

=> A= 3+2².3+...+2¹⁰.3

=> A= 3.(1+2²+...+2¹⁰) chia het cho 3

=> A chia hết cho 3 

 

Answer 3

A=1+2+2+2+..........+2

A=1+2.(1+2)+2.(1+2)+......+2.(1+2)

A=3.3+2.3+...................+2.3

A=3.(3+2+2+....+2) chia hết cho 3